Incompressible surfaces and spunnormal form

TL;DR

This paper proves that any incompressible surface in a cusped hyperbolic 3-manifold, not a virtual fiber, can be isotoped into spunnormal form within an ideal triangulation, extending Thurston's ideas.

Contribution

It establishes a method to isotope incompressible surfaces into spunnormal form in hyperbolic 3-manifolds, generalizing Thurston's approach.

Findings

Incompressible surfaces can be isotoped into spunnormal form

The method applies to surfaces not virtual fibers

Based on Thurston's ideas

Abstract

Suppose M is a cusped finite-volume hyperbolic 3-manifold and T is an ideal triangulation of M with essential edges. We show that any incompressible surface S in M that is not a virtual fiber can be isotoped into spunnormal form in T . The proof is based directly on ideas of W. Thurston.